# PACE: Progressive Angular-to-Norm Contrastive Embedding

arXiv: https://arxiv.org/abs/2609.15152 · HTML: https://mlsanity.com/paper/2609.15152/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [ImageBind: One Embedding Space To Bind Them All](https://mlsanity.com/paper/2305.05665/) (2023)
- [Reproducible scaling laws for contrastive language-image learning](https://mlsanity.com/paper/2212.07143/) (2022)
- [EVA-CLIP: Improved Training Techniques for CLIP at Scale](https://mlsanity.com/paper/2303.15389/) (2023)
- [Precise Zero-Shot Dense Retrieval without Relevance Labels](https://mlsanity.com/paper/2212.10496/) (2022)
- [Qwen3-VL-Embedding and Qwen3-VL-Reranker: A Unified Framework for State-of-the-Art Multimodal Retrieval and Ranking](https://mlsanity.com/paper/2601.04720/) (2026)
- [VLM2Vec: Training Vision-Language Models for Massive Multimodal Embedding Tasks](https://mlsanity.com/paper/2410.05160/) (2024)
- [MM-Embed: Universal Multimodal Retrieval with Multimodal LLMs](https://mlsanity.com/paper/2411.02571/) (2024)
- [BRIGHT: A Realistic and Challenging Benchmark for Reasoning-Intensive Retrieval](https://mlsanity.com/paper/2407.12883/) (2024)
- [MagicLens: Self-Supervised Image Retrieval with Open-Ended Instructions](https://mlsanity.com/paper/2403.19651/) (2024)
- [Gemini Embedding: Generalizable Embeddings from Gemini](https://mlsanity.com/paper/2503.07891/) (2025)
- [mmE5: Improving Multimodal Multilingual Embeddings via High-quality Synthetic Data](https://mlsanity.com/paper/2502.08468/) (2025)
- [UniME-V2: MLLM-as-a-Judge for Universal Multimodal Embedding Learning](https://mlsanity.com/paper/2510.13515/) (2025)
- [GEAR: Granularity-Adaptive Advantage Reweighting for LLM Agents via Self-Distillation](https://mlsanity.com/paper/2605.11853/) (2026)
- [ExpandR: Teaching Dense Retrievers Beyond Queries with LLM Guidance](https://mlsanity.com/paper/2502.17057/) (2025)
- [Improving Contrastive Learning of Sentence Embeddings with Focal-InfoNCE](https://mlsanity.com/paper/2310.06918/) (2023)
- [Flash-VAED: Plug-and-Play VAE Decoders for Efficient Video Generation](https://mlsanity.com/paper/2602.19161/) (2026)
- [When Does Embedding Magnitude Matter? A Cross-Task Functional-Symmetry Framework](https://mlsanity.com/paper/2602.09229/) (2026)

## Built on by (most cited first, 1 of 1)

- [Ovis-Embedding: Pushing the Frontiers of Universal Omni-Modal Embeddings](https://mlsanity.com/paper/2609.25165/) (2026)

## Abstract (arXiv)

Multimodal embedding models encode heterogeneous inputs into a shared embedding space, enabling efficient similarity computation across modalities and tasks. Most existing methods optimize cosine-based contrastive objectives, which promote stable training but restrict semantic compatibility to angular geometry, precluding embedding norms from serving as an additional semantic signal. However, directly optimizing the more expressive dot-product similarity, which leverages both angular and norm information, underperforms cosine-based training and exhibits unstable training dynamics. We attribute this discrepancy to premature optimization-space expansion, manifested as angular--norm entanglement and directional anisotropy in the representation space and further compounded by full-parameter fine-tuning. In this paper, we propose PACE, a two-stage framework that progressively expands both the representation and trainable parameter spaces. Stage I combines cosine-based objective with low-rank adaptation to establish a reliable angular geometry within constrained optimization spaces. Stage II switches to dot-product similarity and full-parameter fine-tuning, enabling embedding directions and norms to jointly encode semantic information. We further introduce Focal Embedding Loss, a confidence-adaptive objective that downweights queries with high positive retrieval confidence while emphasizing ambiguous queries with competitive negatives. Experiments across multiple backbone scales and diverse multimodal embedding tasks consistently validate the effectiveness of PACE.